Answer
$\sqrt{11}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
\dfrac{11}{\sqrt{11}}
,$ multiply both the numerator and the denominator by an expression that will make the denominator a perfect power of the index.
$\bf{\text{Solution Details:}}$
Multiplying both the numerator and the denominator by an expression that will make the denominator a perfect power of the index results to
\begin{array}{l}\require{cancel}
\dfrac{11}{\sqrt{11}}\cdot\dfrac{\sqrt{11}}{\sqrt{11}}
\\\\=
\dfrac{11\sqrt{11}}{\sqrt{11}(\sqrt{11})}
.\end{array}
Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{11\sqrt{11}}{\sqrt{11(11)}}
\\\\=
\dfrac{11\sqrt{11}}{\sqrt{11^2}}
\\\\=
\dfrac{11\sqrt{11}}{11}
\\\\=
\dfrac{\cancel{11}\sqrt{11}}{\cancel{11}}
\\\\=
\sqrt{11}
.\end{array}
